arXiv subjects

Alessandro Frassineti

Publications and source records attributed to Alessandro Frassineti.

4 recordsLinked to original sources

arXiv2026

Prime Fano fourfolds in classical and generalized Grassmannians

We provide a complete classification of Fano fourfolds of Picard rank 1 and index 1 obtained as zero loci of completely reducible homogeneous vector bundles in generalized Grassmannians, i.e. Grassmannians of Dynkin type different from A. This extends the classification done by K\"uchle in standard Grassmannians. In doing so, we exhibit three new families of Fano fourfolds of Picard rank 1 and index 1. For each of the studied Fano fourfolds, we compute several numerical invariants, such as volume and Hodge numbers.

math.AG↗

arXiv2026

Spinorial Fano manifolds

We construct prime Fano manifolds from spin representations of $Spin_n$ for $n\le 14$. In this range, and if $n\ne 13$, the projectivizations of these representations are prehomogeneous, and we deduce that our Fano manifolds are locally rigid and, up to a few exceptions, quasi-homogeneous under the action of their automorphism groups. For $n=13$ we obtain a non-trivial family of minimal compactifications of $SL_3\times SL_3$, modulo some finite group.

math.AG↗

arXiv2026

On Brauer groups of known Enriques manifolds

We compute the Brauer group of some of the known Enriques manifolds. We then build special Brauer-Severi varieties on these manifolds and study the pull-back map from the Brauer group of an Enriques manifold to that of its hyper-K\"ahler universal cover, from both a geometric and an algebraic perspective.

math.AG↗

arXiv2025

Modular vector bundles on hyperk\"ahler manifolds of Debarre-Voisin type

Let X be a very general Debarre--Voisin fourfold. In this article, we prove that all the Schur functors of the restriction of the quotient bundle of Gr(6,10) to X are modular and polystable vector bundles. We also show that the atomic bundles among them are exactly the symmetric powers of the restriction of the quotient bundle. Moreover, we compute the Ext}-groups of different modular vector bundles on X, and we find examples with non-trivial dimensional first Ext}-group.

math.AG↗